5.4 - Dividing Polynomials

5.4 - Dividing Polynomials

Objective

To divide polynomials using synthetic division

Mental Field Trip time

​Back in grade school...

Dividing polynomials

We are going to think about dividing polynomials the same way. We already know that we could factor some quadratic trinomials into two binomial (linear) factors, and then there were some that were not factorable.

We are going to think about those polynomials in terms of "remainder".

Synthetic Division

Synthetic Division

This is an example of a quotient that contains a remainder.

A couple of things:
1) the numbers except the last one are the coefficients of the polynomial quotient.
2) Your firstterm will be one degree less than the
original polynomial.

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What if there are missing terms?

Fill in the Blanks

The remainder of the division problem $\left(k^3-17k+32\right)\div\left(k+5\right)$ is

About that remainder...

It turns out to give us some important information. Take a moment to complete items 1 & 2 on the second page of notes.

Open Ended

Looking at your answers for items 1 & 2, what do you notice? What do you wonder?

Remainder Theorem

Open Ended

Use synthetic substitution to find $$f\left(5\right)\$$ if $$f\left(x\right)=x^3-13x^2+39x-4$$

Poll

Select the image that most closely reflects how you feel about your ability to divide polynomials using synthetic division: